Cursing somebody is asking, even implicitly, that God judge and punish them or at treat them badly. "Damn you" has "God" buried in the meaning, since ultimate judgment isn't up to man. "Damn" is "condemn" (same -demn bit in there), and you're basically asking God to revoke somebody's salvation and sentence them to hell for eternity.
Taking God's name in vain is just using his name in a way that makes no reference to him per se or involves him. "God, that toilet needs cleaning." I'm sure that in saying that, you'd not be telling God anything that he either didn't know or had no interest in knowing. It's abuse of the name, not the person. In the interests of not engaging in this completely by accident, some write "G-d" just in case somebody abuses the name--perhaps by spilling coffee on the paper. It's like saying "al hamdu lillah" over and over, it becomes a meaningless express. So I knew atheists who learned and used it but would never, in English, permit "God bless you" for a sneeze or "thank God" to be left unchallenged; and who were greatly chagrined to learn that they'd been saying "praise to God", and then okay with it since the divinity-portion of the phrase was bleached to meaninglessness.
Blasphemy is another kettle of fish, and that's insulting God.
Profanity would be a fourth thing, and that's just using words that are profane, often scatological. "Hey, dickhead, what the hell you asshole doing fucking with that shit for?" No cursing, no taking God's name in vain, no blasphemy. Just being crude for the sheer sake of being offensive, showing anger, often exaggerated and uncalled for, at people just because they are.
Then there are truly taboo words, where you can't even quote other people's use of them or say, "Okay, team, don't ever say _____" without being accused of insulting vast numbers of people with obvious intent to wound. Unless, of course, you're admitted to the club of those authorized to say it because you're beyond judgment.
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